But there was plenty of shame to be had from West Ham’s performance during their

Actually, it was worse than that: it was embarrassing.

Chelsea’s performance was calm, cool and clinical, yes. But I’ve also rarely seen a team have to work less for a

Sam Allardyce bemoaned individual errors and poor finishing for the Hammers’ latest home hammering. And, yes, Guy Demel’s disastrous back pass that led to the visitors’ opening penalty in the second half that could have halved the deficit to 2-1.

But the problems at Upton Park run far deeper than scapegoats, and it’s time the manager looked a little closer to home.

Then, following a fruitless transfer deadline day in which West Ham failed to secure a striker on loan to cover for the crocked Carroll,

Again, I was slammed on social media. Carroll would be back within weeks, I was told in no uncertain terms. One Twitter user memorably told me that youngster Elliot Lee would score the goals West Ham needed. He’s just returned from a League One loan spell at Colchester (Lee, that is, not the Tweeter).

And so, with almost a third of the season gone, West Ham find themselves out of the relegation zone on goal difference alone, having won just two games from what many considered to be an opening fixture list that bordered on the generous.

Big Sam, as he’s affectionately known, has never enjoyed the West Ham fans’ affection. The respect he rightfully accrued for securing promotion to the Premier League at the first attempt and keeping the side there last season has been gradually eroded by workmanlike performances that must be endured rather than enjoyed.

Sam’s self-aggrandisement has grated, too. , proclaiming his own tactical acumen and preparation in producing a striker-less formation that bamboozled Andre Villas-Boas.

His obdurate decision to turn a surprise tactic into a predictable one resulted in subsequent defeats to Manchester City and Norwich and two goalless draws with Swansea and Aston Villa

The striker-less formation returned two goals in five games. You wouldn’t have needed Nostradamus levels of foresight to see that coming, but the results are now apparently the fault of the players’ performances rather than the manager’s strategy.

Allardyce will point to his lack of options up front, of course, but as manager he has to take a significant share of the blame for this. His insistence to supply the crosses for Carroll was a classic case of putting all your eggs in one basket. Now West Ham don’t even have a basket.

Whispers around Upton Park suggest members of the board wanted to spend the Downing cash on but eventually decided to back their manager instead. Cynics might suggest they were merely giving Allardyce enough rope to hang himself should the need arise.

And now many West Ham fans have come to the conclusion it has. Calls for Allardyce’s head are being taken up across the internet, with everything from his negative tactics to his obdurate faith in woefully out of form captain Kevin Nolan being used as sticks to beat him with.

For many, the very public humiliation of Joe Cole and Jack Collison - both hauled off during the 40th minute of the Chelsea defeat rather than at half-time, has proved the final straw.

There’s no question that relegation would be a disaster for West Ham - something reinforced by the photo op of builders starting work on the club’s new Olympic Stadium home staged last week. And despite David Sullivan and David Gold’s reputation for not firing managers, they’ve already dismissed two since their arrival at Upton Park four years ago.

I would be astonished if they sacked Sam, though, Especially given that three of West Ham’s next four fixtures are against fellow strugglers Fulham, Crystal Palace and Sunderland.

Changing managers mid-season is by no means a sure way of changing fortunes. For every Southampton - and there must be many chairmen casting envious glances at the way Mauricio Pochettino has turned that club around - there are many more Readings and Hulls that remind us that the tactic is very much a gamble.

Yes, a new manager might well shake things up ahead of those crucial six-pointers but equally he could further disrupt a dressing room filled by many of Sam’s signings.

Then there’s the question of who West Ham could bring in. As Crystal Palace have found, there aren’t many top managers around Europe enthralled with the prospect of a Premier League relegation scrap.

Former Hammers hero , of course, but surely that would be a step too far even for owners as much in love of a futile populist gesture as Sullivan and Gold.

Talking of which, only fans with amnesia would sanction an audacious move for Harry Redknapp ahead of a transfer window.

Even if by default, Sam Allardyce deserves his chance to rectify his recent shortcomings and salvage West Ham’s season, securing much-needed points to provide a platform from which he can sign his way out of trouble in January.

Fail to get anything out of those upcoming fixtures, however, and it could well be a different story.